Lectures on Gas Theory

by Ludwig Boltzmann, Stephen G. Brush (editor)

This title is part of UC Press's Voices Revived program, which commemorates University of California Press’s mission to seek out and cultivate the brightest minds and give them voice, reach, and impact. Drawing on a backlist dating to 1893, Voices Revived makes high-quality, peer-reviewed scholarship accessible once again using print-on-demand technology. This title was originally published in 1964.

Genres: Science, Physics, Textbooks

501 pages, Kindle Edition

First published December 1, 1964

About the author

Ludwig Eduard Boltzmann (1844 – 1906) was an Austrian physicist and philosopher whose greatest achievement was in the development of statistical mechanics, which explains and predicts how the properties of atoms (such as mass, charge, and structure) determine the physical properties of matter (such as viscosity, thermal conductivity, and diffusion).

Reviews

[William Bies · Rating 5 out of 5]

Sooner or later every serious student of the kinetic theory ought to get to Ludwig Boltzmann’s original research, as contained in his numerous published memoirs. A good place to start would be the reprint volume edited by Stephen G. Brush (just reviewed by us here), but for reasons of space a good deal of Boltzmann’s contributions had to be omitted there. Boltzmann himself enjoyed a reputation during his lifetime as a masterful teacher at the universities in Graz and later in Vienna, and one can see why in these Vorlesungen über Gastheorie, originally published in 1895 resp. 1898 as the capstone of his entire career. Note: by gas theory he really means thermodynamics and statistical mechanics in general.

The present lectures make for pleasant reading as one takes in Boltzmann’s expansive style, so different from what is the norm these days! The first volume contains a systematic treatment of all of Boltzmann’s signature contributions to kinetic theory, a derivation of his transport equation and the celebrated H-theorem; extensive discussion of the concepts of molecular chaos versus molecular order; and a derivation of the ideal gas law, the law of partial pressures, the mean free path, the shear stress, the diffusion of heat, aerostatics etc. Reading the original it will be apparent that by this stage in his career Boltzmann’s own mind was clear on the meaning of the quantity H and especially on the possibly troubling question as to why thermodynamic and anti-thermodynamic behaviors are not equally likely! Typical of Boltzmann’s ponderous style is a curious mix of heuristic reasoning and hard-core handling of mathematical formulae.

In the second volume, Boltzmann devotes himself to a thorough exposition of Johannes Diderik van der Waals’ pioneering theory of non-ideal gases, or fluids. Clear on the assumptions involved and even clearer on the interpretation of the resulting phase diagram with its critical point. Additional topics include polyatomic gases and a defense of probabilistic methods in mechanics. All around, Volume II evinces a torso-like character in that one really needs quantum mechanics to address its unresolved questions (the problem of equipartition and the specific heats of gases).

The genuine lover of physics must be encouraged to work through these lectures – for the kinetic theory represents a deep insight into the workings of nature and more than anyone else Boltzmann is the one who puts statistical mechanics on a firm foundation. It is always well to watch an original mind in action! For those who would like guidance from a contemporary historian in puzzling out Boltzmann’s obscurities, this reviewer would refer them to Olivier Darrigol’s monograph, Atoms, Mechanics and Probabilities: Ludwig Boltzmann’s Statistico-Mechanical Writings – An Exegesis (Oxford University Press, 2018), which we intend to review ourselves in a moment.

[Medhat ullah · Rating 5 out of 5]

In Lectures on Gas Theory, Ludwig Boltzmann delivers a seminal, ontologically profound treatise that serves as a cornerstone for the mechanistic interpretation of thermodynamic phenomena via kinetic theory. This magnum opus is not merely a compendium of Boltzmann’s investigations but an expansive epistemological framework for understanding the probabilistic underpinnings of entropy and the second law of thermodynamics.At its core, Boltzmann's articulation of the statistical nature of entropy irrevocably dismantles Laplacian determinism, supplanting it with a stochastic paradigm. The text is replete with rigorously axiomatized derivations that leverage Hamiltonian dynamics, Liouville's theorem, and the ergodic hypothesis to bridge the microcanonical ensemble with macroscopic thermodynamic irreversibility. These derivations underscore the entropic arrow of time as an emergent property, rather than an a priori axiom.
Boltzmann’s meticulous elucidation of the H-theorem—derived through a non-trivial application of the Boltzmann equation—remains a paragon of analytical ingenuity. His discourse seamlessly integrates the Boltzmann transport equation's integro-differential formalism with the molecular chaos assumption (Stosszahlansatz), enabling a profound exploration of collisional invariants and distributional relaxation toward equilibrium.The text further ventures into the esoterica of phase space, introducing the conceptual apparatus of coarse-graining and the probabilistic ensemble. Boltzmann’s pioneering work on fluctuations, precursive to the canonical Gibbsian framework, illuminates the nuanced interplay between determinism and probabilistic behavior in thermodynamic systems.Despite its epochal contributions, Lectures on Gas Theory is not without its interpretive labyrinths. The ontological implications of Boltzmann’s probabilistic worldview—particularly the controversial Boltzmann brain hypothesis—spawn enduring debates on the cosmological viability of entropy and the temporal finitude of statistical equilibria.